algebra Aug 28, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
If Γ \Gamma Γ is a non-coHopfian property-(T) group and G G G is its ascending HNN extension, then the full group algebra C ∗ ( G ) C^*(G) C ∗ ( G ) is not finite. Indeed, Kazhdan projections p H < p Γ p_H<p_\Gamma p H < p Γ become unitarily equivalent under the stable letter, which cannot occur inside a finite C ∗ C^* C ∗ -algebra.
For
W = ( ⨁ G / Γ Z / 2 Z ) ⋊ G ,
W=\left(\bigoplus_{G/\Gamma}\mathbb Z/2\mathbb Z\right)\rtimes G,
W = G /Γ ⨁ Z /2 Z ⋊ G ,
the paper proves more strongly that every homomorphism…
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combinatorics Sep 2, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
Let P ⊆ Q n P\subseteq Q_n P ⊆ Q n be convex. Williams proves the stronger statement that for every k ≥ 0 k\ge0 k ≥ 0 ,
w ( P × Q k ) ≥ w ( Q n + k ) ∣ P ∣ 2 − n ,
w(P\times Q_k)
\ge
w(Q_{n+k})\,|P|\,2^{-n},
w ( P × Q k ) ≥ w ( Q n + k ) ∣ P ∣ 2 − n ,
where w w w denotes poset width.
Taking k = 0 k=0 k = 0 gives
w ( P ) ≥ ∣ P ∣ ( n ⌊ n / 2 ⌋ ) 2 − n ,
w(P)\ge
|P|\binom{n}{\lfloor n/2\rfloor}2^{-n},
w ( P ) ≥ ∣ P ∣ ( ⌊ n /2 ⌋ n ) 2 − n ,
which is exactly the Daykin-Frankl conjecture.
The proof proceeds by induction on n n n , reducing the step to a structural lemma for a convex subset of R × Q 1 R\times Q_1 R × Q 1 and…
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analysis Sep 2, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
For every neighborhood U U U of the origin in C × R \mathbb{C}\times\mathbb{R} C × R and every ε > 0 \varepsilon>0 ε > 0 , Curry constructs a smooth nonnegative perturbation ϕ \phi ϕ , supported in U U U with ∥ ϕ ∥ C 2 < ε \|\phi\|_{C^2}<\varepsilon ∥ ϕ ∥ C 2 < ε , such that
T ϕ 0 , 1 = span C { L ϕ }
T^{0,1}_\phi=\operatorname{span}_{\mathbb C}\{L_\phi\}
T ϕ 0 , 1 = span C { L ϕ }
is strongly pseudoconvex, its canonical bundle admits a nowhere-zero closed section, yet every C 1 C^1 C 1 CR function near the origin satisfie…
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combinatorics Sep 3, 2026 Significance 25/100 Registry: unreviewed
disproved → disproved
VibeMathed recorded: The Near-Quadratic Elekes-Ronyai Expander Conjecture. Consult the linked registry entry for the original report and scope.
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quantum-information-computing Jul 28, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
VibeMathed recorded: Existence of Bipartite Bound Information. Consult the linked registry entry for the original report and scope.
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combinatorics Jul 27, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
VibeMathed recorded: Unimodality of Kazhdan-Lusztig Polynomials of Matroids. Consult the linked registry entry for the original report and scope.
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quantum-information-computing Aug 13, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
Establishes that every PPT channel is eventually entanglement-breaking (finite EB index), in full generality, and bounds the index by 3 uniformly in dimension for a family strictly containing the 2-superpositive maps. The PPT-squared conjecture itself - index at most 2 - remains open; the paper presents its results as strong evidence toward the cubed version.
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analysis Aug 5, 2026 Significance 25/100 Registry: lean checked
Prior state unknown → proved
VibeMathed recorded: Gabor Frames of Totally Positive Functions. Consult the linked registry entry for the original report and scope.
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analysis Jul 26, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
negative below the 1/3 threshold; the endpoint case is still open
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analysis Aug 3, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
VibeMathed recorded: Kalton-Peck Space and its Hyperplanes. Consult the linked registry entry for the original report and scope.
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analysis Jul 9, 2026 Significance 25/100 Registry: lean verified
Prior state unknown → disproved
VibeMathed recorded: Strichartz's Question on Fourier Frames for the Cantor Measure. Consult the linked registry entry for the original report and scope.
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analysis Jun 14, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
in the range s in (1/4,1); Brezis's Problem 5.4 outside that range is untouched
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geometry-topology Jun 16, 2026 Significance 25/100 Registry: site confirmed
Prior state unknown → disproved
VibeMathed recorded: Wegner's Piercing Conjecture for Rectangles. Consult the linked registry entry for the original report and scope.
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combinatorics Jul 23, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
VibeMathed recorded: Stanley's Claw-Free Schur-Positivity Conjecture. Consult the linked registry entry for the original report and scope.
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theoretical-computer-science Jul 31, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
VibeMathed recorded: Sharp Hardness for MAX-3-CUT. Consult the linked registry entry for the original report and scope.
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theoretical-computer-science Apr 2, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
VibeMathed recorded: Bipartite Exact Matching in P. Consult the linked registry entry for the original report and scope.
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algorithms-optimization Aug 3, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
VibeMathed recorded: Approximating Two-Terminal Network Reliability. Consult the linked registry entry for the original report and scope.
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analysis May 17, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
VibeMathed recorded: Maz'ya's Question on Distinguishing Two Maximal Operators. Consult the linked registry entry for the original report and scope.
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geometry-topology Jul 13, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
rules out the two-point LP method in this dimension; the optimal packing in dimension 36 remains unknown
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combinatorics Jul 10, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
VibeMathed recorded: A Counterexample to Nivat's Conjecture for a Non-Convex Window. Consult the linked registry entry for the original report and scope.
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quantum-information-computing Jul 23, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
VibeMathed recorded: Unconditional One-Bit Unclonable Encryption. Consult the linked registry entry for the original report and scope.
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analysis Aug 7, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
VibeMathed recorded: A counterexample to the Howland-Kato problem for positive commutators. Consult the linked registry entry for the original report and scope.
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analysis Aug 11, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
Strict convexity and real-analytic boundaries are what make this sharp: the classical Gordon-Webb-Wolpert drums are non-convex polygons, so the obvious escape routes are closed off.
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combinatorics Mar 10, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
Records, not resolutions: the exact values of these Ramsey numbers remain unknown.
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algebra Aug 14, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
VibeMathed recorded: The Cone Theorem for Effective Fourfold Pairs in Characteristic p > 5 p > 5 p > 5 . Consult the linked registry entry for the original report and scope.
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differential-equations Aug 11, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
Tensorisation and parabolic rescaling carry the one-dimensional example to real symmetric isotropic counterexamples on R^d and on every bounded domain, in every dimension.
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algebra Jul 21, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
VibeMathed recorded: Counterexamples to the xz-Conjecture and the Mathieu Conjecture for SU(2). Consult the linked registry entry for the original report and scope.
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combinatorics May 23, 2026 Significance 25/100 Registry: site confirmed
Prior state unknown → disproved
VibeMathed recorded: Simon's Extendable Shellability Conjecture. Consult the linked registry entry for the original report and scope.
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number-theory May 1, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
VibeMathed recorded: The Banks-Martin Conjecture on Primitive Sets. Consult the linked registry entry for the original report and scope.
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algebra Jul 31, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
The counterexample is an ordinary algebra concentrated in degree zero, with the strongest possible vanishing in positive degrees, so the phenomenon needs no grading or differential. Liu and Shen had already disproved the differential-graded version in December 2025 without any AI involvement; the classical case is the one that fell with a model in the loop.
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combinatorics Jun 16, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
in polynomial edge-density regimes; the general question remains open
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algebra Jul 26, 2026 Significance 25/100 Registry: lean verified
Prior state unknown → proved
VibeMathed recorded: Explicit Presentation of the 2-adic Absolute Galois Group. Consult the linked registry entry for the original report and scope.
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geometry-topology Aug 1, 2026 Significance 25/100 Registry: lean verified
Prior state unknown → proved
VibeMathed recorded: Ehrhart's Volume Conjecture. Consult the linked registry entry for the original report and scope.
● Source○ Replay○ Reproduced● Formal proof○ Statement audit○ External check○ Expert review○ Peer review
probability-statistics Jul 20, 2026 Significance 25/100 Registry: site confirmed
Prior state unknown → disproved
Explicit counterexamples in dimensions 3 and 4, so GMC(n) fails for every n >= 3; GMC(1) was already known, and a separate human-authored preprint claims the remaining n = 2 case affirmatively
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algebra Jul 30, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → proved
VibeMathed recorded: Local Cohomology Modules With Nonclosed Support. Consult the linked registry entry for the original report and scope.
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algebra Jul 21, 2026 Significance 25/100 Registry: unreviewed
Prior state unknown → disproved
VibeMathed recorded: Batyrev's Stringy Hodge Number Conjecture. Consult the linked registry entry for the original report and scope.
● Source○ Replay○ Reproduced○ Formal proof○ Statement audit○ External check○ Expert review○ Peer review